How many times did italy change sides during world war 2 and why?

Here is the explanation,

July 1943

Italian leader Benito Mussolini was arrested and replaced with Marshal Pietro Badoglio. Badoglio immediately began secret negotiations with the Allies.

September 1943

The Allies invaded Italy and the Badoglio government signed an armistice. Italy declared war on Germany and joined the Allies.

However, the German military still occupied much of Italy and continued to fight. The Italian Social Republic, a puppet state of Germany, was established in northern Italy. The Italian Social Republic continued to fight alongside Germany until the end of the war.